On nonparametric estimation in nonlinear AR(1)-models
type: Item
instance of: scholarly article
title: On nonparametric estimation in nonlinear AR(1)-models
zbMATH Open document ID: 0954.62049
DOI: 10.1016/S0167-7152(98)00289-2
published in: Statistics \& Probability Letters
publication date: 2001-01-30T00:00:00Z
review text: This paper considers the estimation problem of the mean function and the conditional variance (the volatility function) of a nonlinear first-order autoregressive model nonparametrically. Minimax rates of convergence are established over a scale of Besov bodies \({\mathcal B}_{spq}\) and a range of global \(L_{p'}\) error measurements, for \(1\leq p' \leq \infty.\) The estimation procedure is based on a martingale regression approximation scheme. Adaptation results with respect to an unknown degree of smoothness are obtained. The authors make use of a systematic time evolving signal plus noise analogy. This emphazises the closeness of AR(1) models to more tractable models such as nonparametric regression.
reviewed by: Vyacheslav A. Vasiliev
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 1395117
zbMATH Keywords: minimax estimation
zbMATH Keywords: adaptive estimation
zbMATH Keywords: weak dependence
zbMATH Keywords: time series
author: M. Hoffmann
MaRDI profile type: Publication
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full work available at URL: s0167-7152(98)00289-2
OpenAlex ID: W2031036493
description: scientific article; zbMATH DE number 1395117